Periodic Reporting for period 1 - MesoComp (Order at the Mesoscale: Connecting supercomputing of compressible convection to classical and quantum machine learning)
Reporting period: 2023-01-01 to 2025-06-30
Turbulent convection flows in nature display prominent patterns in the mesoscale range whose characteristic length in the horizontal directions exceeds the system scale height, despite the fact that turbulent fluid motion typically implies a very stochastic and irregular behaviour. Known as the turbulent superstructure of convection, they are absent on both larger and smaller scales and evolve in ways not yet understood; but they are an essential link in the heat and momentum transport to larger scales, an important driver of intermittent fluid motion at sub-mesoscales, and one major source of uncertainty in the prognosis of climate change and space weather. In MesoComp, we investigate the formation of superstructures in massively parallel simulations of compressible turbulent convection in horizontally extended domains, aiming for a deeper understanding of their dynamical origin and role in the transport of heat and momentum. We use these high-fidelity simulations to build recurrent machine learning models to predict the evolution and statistics of the superstructure and thus quantify the transport fluxes beyond the mesoscale. Furthermore, we analyse the impact of the mesoscale structures on the highly intermittent statistics at the small-scale of the flow and reveal the resulting feedback in the form of improved subgrid parametrizations by means of recurrent and generative machine learning. MesoComp opens additional doors to the application of quantum algorithms in machine learning which significantly improve the statistical sampling and data compression properties compared to their classical counterparts. From a longer-term perspective, this research results in a quantum advantage for the numerical analysis of classical turbulence, which accelerates the parametrizations of mesoscale convection and increases their fidelity. This work will finally lead to more precise predictions of the on-going climate change and global warming. The results will also improve solar activity models and thus solar storm prognoses with impacts on satellite communication and electrical grids.
The present scientific progress of the project MesoComp, which started in January 2023, can be summarized by the following work performed and main achievements. (1) Large-scale numerical simulations of mesoscale convection, a turbulence which is driven by buoyancy forces, revealed for the first time a hierarchical and self-similar structure of the flow patterns. This structural hierarchy starts from a network of unstable hot patches of rising fluid near the ground (see Fig_mesoscale.jpg) and proceeds to a large-scale order of flow circulations at the mesoscale, the outer scale in the simulations. These high-resolution simulations and their analysis were conducted on Europe’s fastest GPU-accelerated supercomputers and required new ways of on-the-fly analysis of the massive stream of data. (2) Additional compressibility of the fluid motion enhances the intermittent fluctuations of the turbulence fields at the smallest scales due to the formation of pre-shocks and shocks (see Fig_compressible.png). We systematically quantified these fluctuations, their importance for the turbulent mixing, and their dependence on the vigor of turbulence, which is measured by the Rayleigh number in convection. (3) We demonstrated that classical and quantum reservoir computing frameworks can serve as scalable reduced order models to represent the complex turbulent mixing at unresolved scales of mesoscale convection. We started to investigate how their performance depends sensitively on the reservoir network structure by applying measures to quantify the information processing capacity of the networks and the correlations of the qubits in the classical and quantum cases, respectively. (4) First proof-of-concept studies of generative quantum machine learning algorithms applied to the transport of tracer particles in turbulence have been finalized recently. They demonstrate clearly the potential of this class of methods as a convective parametrization. (5) We also explored the performance of our developed quantum algorithms on real quantum hardware for simple use cases to estimate the error rates and coherence times of the quantum computers. Such a simple fluid flow problem is illustrated in Fig_quantum.png. The research along all these lines will be continued in the coming years of the MesoComp project.
Our supercomputing simulations of mesoscale convection produced high-quality data which display systematic trends for the velocity and temperature fluctuations in convection flows in plane-layer configurations, i.e. exactly those configurations that approximate the geometry of natural flows best. We could show for the first time that the boundary layers are organized in a hierarchical bottom-up way for Rayleigh numbers that were not obtained in this configuration before. In this respect, our results shift paradigms. To this end, we demonstrate a structure formation that is initiated by many local instabilities near the wall in parallel which then successively cluster and aggregate to bigger fluid motions further away from the bounding walls. Such a bottom-up scenario is present in several other complex systems in nature, e.g. in the human brain neuron network. These results also challenge the concept of an ultimate regime of turbulent convection at very high Rayleigh numbers, which would be in line with a global flow instability of the near-wall region of the convection layer, proceeding as a whole. Our findings were partly unexpected, in particular that the rising fluid patches form a self-similar network for the wide range of Rayleigh numbers which were studied. Our numerical simulations also revealed details on the fluid motion that are not accessible in laboratory experiments at high Rayleigh numbers anymore.